0
Research Papers

A Fully Coupled Theory and Variational Principle for Thermal–Electrical–Chemical–Mechanical Processes

[+] Author and Article Information
Pengfei Yu

State Key Laboratory for Strength and
Vibration of Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: yupf9570@stu.xjtu.edu.cn

Shengping Shen

State Key Laboratory for Strength and
Vibration of Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: sshen@mail.xjtu.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 20, 2014; final manuscript received September 8, 2014; accepted manuscript posted September 11, 2014; published online September 24, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(11), 111005 (Sep 24, 2014) (12 pages) Paper No: JAM-14-1323; doi: 10.1115/1.4028529 History: Received July 20, 2014; Revised September 08, 2014; Accepted September 11, 2014

Thermal–electrical–chemical–mechanical coupling controls the behavior of many transport and electrochemical reactions processes in physical, chemical and biological systems. Hence, advanced understanding of the coupled behavior is crucial and attracting a large research interest. However, most of the existing coupling theories are limited to the partial coupling or particular process. In this paper, on the basis of irreversible thermodynamics, a variational principle for the thermal electrical chemical mechanical fully coupling problems is proposed. The complete fully coupling governing equations, including the heat conduction, mass diffusion, electrochemical reactions and electrostatic potential, are derived from the variational principle. Here, the piezoelectricity, conductivity, and electrochemical reactions are taken into account. Both the constitutive relations and evolving equations are fully coupled. This theory can be used to deal with coupling problems in solids, including conductors, semiconductors, piezoelectric and nonpiezoelectric dielectrics. As an application of this work, a developed boundary value problem is solved numerically in a mixed ion-electronic conductor (MIEC). Numerical results show that the coupling between electric field, diffusion, and chemical reactions influence the defect distribution, electrostatic potential and mechanical stress.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Demirel, Y., 2008, “Modeling of Thermodynamically Coupled Reaction-Transport Systems,” Chem. Eng. J., 139(1), pp. 106–117. [CrossRef]
Demirel, Y., 2009, “Thermodynamically Coupled Heat and Mass Flows in a Reaction-Transport System With External Resistances,” Int. J. Heat Mass Transfer, 52(7–8), pp. 2018–2025. [CrossRef]
Rambert, G., Grandidier, J.-C., and Aifantis, E. C., 2007, “On the Direct Interactions Between Heat Transfer, Mass Transport and Chemical Processes Within Gradient Elasticity,” Eur. J. Mech.—A/Solids, 26(1), pp. 68–87. [CrossRef]
Suo, Y., and Shen, S., 2013, “General Approach on Chemistry and Stress Coupling Effects During Oxidation,” J. Appl. Phys., 114(16), p. 164905. [CrossRef]
Dong, X., Feng, X., and Hwang, K.-C., 2012, “Oxidation Stress Evolution and Relaxation of Oxide Film/Metal Substrate System,” J. Appl. Phys., 112(2), p. 023502. [CrossRef]
Dong, X., Fang, X., Feng, X., and Hwang, K. C., 2013, “Diffusion and Stress Coupling Effect During Oxidation at High Temperature,” J. Am. Ceram. Soc., 96(1), pp. 44–46. [CrossRef]
Tuller, H. L., and Bishop, S. R., 2011, “Point Defects in Oxides: Tailoring Materials Through Defect Engineering,” Annu. Rev. Mater. Res., 41(1), pp. 369–398. [CrossRef]
Kalinin, S. V., and Spaldin, N. A., 2013, “Materials Science. Functional Ion Defects in Transition Metal Oxides,” Science, 341(6148), pp. 858–859. [CrossRef] [PubMed]
Swaminathan, N., Qu, J., and Sun, Y., 2007, “An Electrochemomechanical Theory of Defects in Ionic Solids. I. Theory,” Philos. Mag., 87(11), pp. 1705–1721. [CrossRef]
Swaminathan, N., Qu, J., and Sun, Y., 2007, “An Electrochemomechanical Theory of Defects in Ionic Solids. Part II. Examples,” Philos. Mag., 87(11), pp. 1723–1742. [CrossRef]
Jesse, S., Balke, N., Eliseev, E., Tselev, A., Dudney, N. J., Morozovska, A. N., and Kalinin, S. V., 2011, “Direct Mapping of Ionic Transport in a Si Anode on the Nanoscale: Time Domain Electrochemical Strain Spectroscopy Study,” ACS Nano, 5(12), pp. 9682–9695. [CrossRef] [PubMed]
Jesse, S., Kumar, A., Arruda, T. M., Kim, Y., Kalinin, S. V., and Ciucci, F., 2012, “Electrochemical Strain Microscopy: Probing Ionic and Electrochemical Phenomena in Solids at the Nanometer Level,” MRS Bull., 37(7), pp. 651–658. [CrossRef]
Kumar, A., Jesse, S., Morozovska, A. N., Eliseev, E., Tebano, A., Yang, N., and Kalinin, S. V., 2013, “Variable Temperature Electrochemical Strain Microscopy of Sm-Doped Ceria,” Nanotechnology, 24(14), p. 145401. [CrossRef] [PubMed]
Nowacki, W., 1974, “Dynamic Problems of Thermodiffusion in Elastic Solids,” Proc. Vib. Problems, 15(2), pp. 105–128.
Kuang, Z.-B., 2007, “Some Problems in Electrostrictive and Magnetostrictive Materials,” Acta Mech. Solida Sin., 20(3), pp. 219–227. [CrossRef]
Kuang, Z.-B., 2007, “Some Variational Principles in Elastic Dielectric and Elastic Magnetic Materials,” Eur. J. Mech.—A/Solids, 27(3), pp. 504–514. [CrossRef]
Kuang, Z.-B., 2008, “Variational Principles for Generalized Dynamical Theory of Thermopiezoelectricity,” Acta Mech., 203(1–2), pp. 1–11. [CrossRef]
Fischer, F., Svoboda, J., and Petryk, H., 2014, “Thermodynamic Extremal Principles for Irreversible Processes in Materials Science,” Acta Mater., 67, pp. 1–20. [CrossRef]
Hu, S., and Shen, S., 2013, “Non-Equilibrium Thermodynamics and Variational Principles for Fully Coupled Thermal–Mechanical–Chemical Processes,” Acta Mech., 224(12), pp. 2895–2910. [CrossRef]
De Groot, S. R., and Mazur, P., 2013, Non-Equilibrium Thermodynamics, Courier Dover Publications, New York.
Prigogine, I., and Kondepudi, D., 1999, “Thermodynamique,” Editions Odile Jacob, Paris, France.
Kuang, Z.-B., 1993, Nonlinear Continuum Mechanics, Xi'an Jiaotong University Press, Xi'an, China.
Liu, M., and Winnick, J., 1999, “Fundamental Issues in Modeling of Mixed Ionic-Electronic Conductors (MIECs),” Solid State Ionics, 118(1), pp. 11–21. [CrossRef]
Gigliotti, M., and Grandidier, J.-C., 2010, “Chemo-Mechanics Couplings in Polymer Matrix Materials Exposed to Thermo-Oxidative Environments,” Comptes Rendus Mécanique, 338(3), pp. 164–175. [CrossRef]
Chen, Z., 2004, “Comparison of the Mobile Charge Distribution Models in Mixed Ionic-Electronic Conductors,” J. Electrochem. Soc., 151(10), p. A1576. [CrossRef]
Atkinson, A., 1997, “Chemically-Induced Stresses in Gadolinium-Doped Ceria Solid Oxide Fuel Cell Electrolytes,” Solid State Ionics, 95(3–4), pp. 249–258. [CrossRef]
Hayashi, H., Kanoh, M., Quan, C. J., Inaba, H., Wang, S., Dokiya, M., and Tagawa, H., 2000, “Thermal Expansion of Gd-Doped Ceria and Reduced Ceria,” Solid State Ionics, 132(3), pp. 227–233. [CrossRef]
Zhou, H., Qu, J., and Cherkaoui, M., 2010, “Finite Element Analysis of Oxidation Induced Metal Depletion at Oxide–Metal Interface,” Comput. Mater. Sci., 48(4), pp. 842–847. [CrossRef]
Atkinson, A., and Ramos, T., 2000, “Chemically-Induced Stresses in Ceramic Oxygen Ion-Conducting Membranes,” Solid State Ionics, 129(1), pp. 259–269. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Configuration of the cross section of a planar electrolyte with all four edges fixed

Grahic Jump Location
Fig. 2

Comparison among the present model with a = 0 and Swaminathan et al. [10]

Grahic Jump Location
Fig. 3

Vacancy distribution for different applied voltages for (a) a = 5×10-12 and (b) a = 1×10-11

Grahic Jump Location
Fig. 4

Vacancy distribution for different a for (a) V = 0, (b) V = 0.5, and (c) V = 1.01

Grahic Jump Location
Fig. 5

Oxygen concentration for different applied voltages for (a) a = 0, (b) a = 5 × 10-12, and (c) a = 1 × 10-11

Grahic Jump Location
Fig. 6

Oxygen concentration for different a for (a) V = 0, (b) V = 0.5, and (c) V = 1.01

Grahic Jump Location
Fig. 7

Distribution of nondimensional electrostatic potentials for different applied voltages for (a) a = 0, (b) a = 5 × 10-12, and (c) a = 1 × 10-11

Grahic Jump Location
Fig. 8

Distribution of nondimensional electrostatic potentials for different a for (a) V = 0, (b) V = 0.5, and (c) V = 1.01

Grahic Jump Location
Fig. 9

Stress distribution for different applied voltages for (a) a = 0, (b) a = 5 × 10-12, and (c) a = 1 × 10-11

Grahic Jump Location
Fig. 10

Stress distribution for different a for (a) V = 0, (b) V = 0.5, and (c) V = 1.01

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In